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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="modelc_2.html#NM3" title="MODELC_2:NM.3">LTLModel</a><br/>  for <font color="Olive" title="b2">Kai</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>, the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">BasicAssign</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">f1</font>, <font color="Olive" title="b4">f2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b3">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">Kai</font> &amp; <font color="Olive" title="b4">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">Kai</font> holds <br/> for <font color="Olive" title="b5">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b3">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="modelc_2.html#NM3" title="MODELC_2:NM.3">LTLModel</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Kai</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>, the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">BasicAssign</a> of <font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b2">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">Kai</font> &amp; <font color="Olive" title="b3">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">Kai</font> holds <br/> for <font color="Olive" title="b4">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b4">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">Kai</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K15" title="MODELC_2:func.15">atomic_LTL</a>, the <a href="modelc_2.html#U1" title="MODELC_2:sel.1">BasicAssign</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> &amp; <font color="Olive" title="b2">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> holds <br/> for <font color="Olive" title="b3">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b1">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">H</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f1</font>, <font color="Maroon" title="c5">f2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_2.html#K9" title="MODELC_2:func.9">LTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> &amp; <font color="Maroon" title="c5">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> implies  for <font color="Olive" title="b1">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> )</span><br/>









<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>] <span class="kw">means </span>( <font color="Maroon" title="c4">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> $1,<font color="Maroon" title="c3">Kai</font> &amp; <font color="Maroon" title="c5">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> $1,<font color="Maroon" title="c3">Kai</font> implies  for <font color="Olive" title="b1">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 holds <br/><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> );<br/>
<a NAME="E1:99"/><span class="lab"><font color="Green" title="E67">A1</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="99_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:99_1"/><span class="lab"><font color="Green" title="E68">A2</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">k</font>]
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:99_1"/><span class="lab"><font color="Green" title="E69">A3</font></span>: 
<font color="Maroon" title="c4">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1,<font color="Maroon" title="c3">Kai</font>
 <span class="kw">and </span><br/><a NAME="E3:99_1"/><span class="lab"><font color="Green" title="E70">A4</font></span>: 
<font color="Maroon" title="c5">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1,<font color="Maroon" title="c3">Kai</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 holds <br/><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c7">H</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 implies <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> )</span><br/>

<span class="kw">assume </span><a NAME="E4:99_1"/><span class="lab"><font color="Green" title="E71">A5</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:99_1_1"/>
( <font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a>  or <font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a>  or <font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a>  or <font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>  or <font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  or <font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  or <font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T2" target="_self" onmouseover="rs('modelc_2/T2')" onmouseout="rh()">Th2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:99_1_1_1"/><span class="lab"><font color="Green" title="E72">A6</font></span>: 
<font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:99_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:99_1_1_1"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_1"><span class="lab"><font color="Green" title="E72">A6</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:99_1_1_2"/><span class="lab"><font color="Green" title="E72">A7</font></span>: 
<font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:99_1_1_2"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T10" target="_self" onmouseover="rs('modelc_2/T10')" onmouseout="rh()">Th10</a></span>;<br/><a NAME="E3:99_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A8</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
 the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_2"><span class="lab"><font color="Green" title="E72">A7</font></span></a></span>
<br/>.= 
 the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E3:99_1_1_2"><span class="lab"><font color="Green" title="E73">A8</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E5:99_1_1_2"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_2"><span class="lab"><font color="Green" title="E72">A7</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:99_1_1_3"/><span class="lab"><font color="Green" title="E72">A9</font></span>: 
<font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:99_1_1_3"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T10" target="_self" onmouseover="rs('modelc_2/T10')" onmouseout="rh()">Th10</a></span>;<br/><a NAME="E3:99_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A10</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
 the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">NEXT</a> of <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_3"><span class="lab"><font color="Green" title="E72">A9</font></span></a></span>
<br/>.= 
 the <a href="modelc_2.html#U2" title="MODELC_2:sel.2">NEXT</a> of <font color="Maroon" title="c2">V</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K10" title="MODELC_2:func.10">the_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E3:99_1_1_3"><span class="lab"><font color="Green" title="E73">A10</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E5:99_1_1_3"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_3"><span class="lab"><font color="Green" title="E72">A9</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_4"><span class="kw">suppose </span></a><a NAME="E1:99_1_1_4"/><span class="lab"><font color="Green" title="E72">A11</font></span>: 
<font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:99_1_1_4"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E3:99_1_1_4"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><a NAME="E4:99_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A12</font></span>: 
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>;<br/><a NAME="E5:99_1_1_4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1_1_4"><span class="lab"><font color="Green" title="E72">A11</font></span></a>, <a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E6:99_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A13</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
 the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_4"><span class="lab"><font color="Green" title="E72">A11</font></span></a></span>
<br/>.= 
 the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <font color="Maroon" title="c2">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1_1_4"><span class="lab"><font color="Green" title="E73">A12</font></span></a>, <a class="txt" href="#E6:99_1_1_4"><span class="lab"><font color="Green" title="E74">A13</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E8:99_1_1_4"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_4"><span class="lab"><font color="Green" title="E72">A11</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_5"><span class="kw">suppose </span></a><a NAME="E1:99_1_1_5"/><span class="lab"><font color="Green" title="E72">A14</font></span>: 
<font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:99_1_1_5"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E3:99_1_1_5"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><a NAME="E4:99_1_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A15</font></span>: 
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>;<br/><a NAME="E5:99_1_1_5"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1_1_5"><span class="lab"><font color="Green" title="E72">A14</font></span></a>, <a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E6:99_1_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A16</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
 the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_5"><span class="lab"><font color="Green" title="E72">A14</font></span></a></span>
<br/>.= 
 the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <font color="Maroon" title="c2">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1_1_5"><span class="lab"><font color="Green" title="E73">A15</font></span></a>, <a class="txt" href="#E6:99_1_1_5"><span class="lab"><font color="Green" title="E74">A16</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E8:99_1_1_5"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_5"><span class="lab"><font color="Green" title="E72">A14</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_6"><span class="kw">suppose </span></a><a NAME="E1:99_1_1_6"/><span class="lab"><font color="Green" title="E72">A17</font></span>: 
<font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:99_1_1_6"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E3:99_1_1_6"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><a NAME="E4:99_1_1_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A18</font></span>: 
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>;<br/><a NAME="E5:99_1_1_6"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1_1_6"><span class="lab"><font color="Green" title="E72">A17</font></span></a>, <a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E6:99_1_1_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A19</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
 the <a href="modelc_2.html#U3" title="MODELC_2:sel.3">UNTIL</a> of <font color="Maroon" title="c2">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_6"><span class="lab"><font color="Green" title="E72">A17</font></span></a></span>
<br/>.= 
 the <a href="modelc_2.html#U3" title="MODELC_2:sel.3">UNTIL</a> of <font color="Maroon" title="c2">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1_1_6"><span class="lab"><font color="Green" title="E73">A18</font></span></a>, <a class="txt" href="#E6:99_1_1_6"><span class="lab"><font color="Green" title="E74">A19</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E8:99_1_1_6"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_6"><span class="lab"><font color="Green" title="E72">A17</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="99_1_1_7"><span class="kw">suppose </span></a><a NAME="E1:99_1_1_7"/><span class="lab"><font color="Green" title="E72">A20</font></span>: 
<font color="Maroon" title="c7">H</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font></span><br/><div class="add"><a NAME="E2:99_1_1_7"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E3:99_1_1_7"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><a NAME="E4:99_1_1_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A21</font></span>: 
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>;<br/><a NAME="E5:99_1_1_7"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1_1_7"><span class="lab"><font color="Green" title="E72">A20</font></span></a>, <a class="ref" href="modelc_2.html#T11" target="_self" onmouseover="rs('modelc_2/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E6:99_1_1_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A22</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="modelc_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> = 
 the <a href="modelc_2.html#U4" title="MODELC_2:sel.4">RELEASE</a> of <font color="Maroon" title="c2">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_7"><span class="lab"><font color="Green" title="E72">A20</font></span></a></span>
<br/>.= 
 the <a href="modelc_2.html#U4" title="MODELC_2:sel.4">RELEASE</a> of <font color="Maroon" title="c2">V</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c7">H</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:99_1"><span class="lab"><font color="Green" title="E68">A2</font></span></a>, <a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E3:99_1"><span class="lab"><font color="Green" title="E70">A4</font></span></a>, <a class="txt" href="#E4:99_1_1_7"><span class="lab"><font color="Green" title="E73">A21</font></span></a>, <a class="txt" href="#E6:99_1_1_7"><span class="lab"><font color="Green" title="E74">A22</font></span></a>, <a class="txt" href="modelc_2.html#E101"><span class="lab"><font color="Green" title="E65">Lm23</font></span></a></span>
;<br/><span class="kw">hence </span><a NAME="E8:99_1_1_7"/>
<font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99_1"><span class="lab"><font color="Green" title="E69">A3</font></span></a>, <a class="txt" href="#E4:99_1"><span class="lab"><font color="Green" title="E71">A5</font></span></a>, <a class="txt" href="#E1:99_1_1_7"><span class="lab"><font color="Green" title="E72">A20</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E2:99"/><span class="lab"><font color="Green" title="E68">A23</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T3" target="_self" onmouseover="rs('modelc_2/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<a NAME="E3:99"/>
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S2" onmouseover="rs('nat_1/S2')" onmouseout="rh()">NAT_1:sch 2</a>(<a class="txt" href="#E2:99"><span class="lab"><font color="Green" title="E68">A23</font></span></a>, <a class="txt" href="#E1:99"><span class="lab"><font color="Green" title="E67">A1</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E4:99"/>
( <font color="Maroon" title="c4">f1</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> &amp; <font color="Maroon" title="c5">f2</font> <a href="modelc_2.html#R5" title="MODELC_2:pred.5">is-PreEvaluation-for</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">Kai</font> implies  for <font color="Olive" title="b1">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Maroon" title="c4">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">H</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
